Linear Equations

Q Just what is a "system of linear equations in two unknowns?"
A First, a linear equation in two unknowns x and y is an equation of the form
ax + by = c
where a, b, and c are numbers, and where a and b are not both zero.

Examples: Linear Equations:
4x + 5y = 0
This has a = 4, b = 5, c = 0
x - y = 11
This has a = 1, b = -1, c = 11
4x = 3
This has a = 4, b = 0, c = 3

Second, a system of linear equations is just a collection of these beasts. To solve a system of linear equations means to find a solution (or solutions) (x, y) that simultaneously satisfies all of the equations in the system.

Example: System of Linear Equations:
4x + 5y = 40 x-y = 1
This is a system of two linear equations with solution x = 5, y = 4. We can also write the solution as (5, 4)